Question
Answer
$$(5z^2+2)^4=625z^8+1000z^6+600z^4+160z^2+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5z^2+2)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}625z^8+1000z^6+600z^4+160z^2+16\end{aligned} $$ | |
| ① | $$ (5z^2+2)^4 = (5z^2+2)^2 \cdot (5z^2+2)^2 $$ |
| ② | Find $ \left(5z^2+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5z^2 } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(5z^2+2\right)^2 = \color{blue}{\left( 5z^2 \right)^2} +2 \cdot 5z^2 \cdot 2 + \color{red}{2^2} = 25z^4+20z^2+4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{25z^4+20z^2+4}\right) $ by each term in $ \left( 25z^4+20z^2+4\right) $. $$ \left( \color{blue}{25z^4+20z^2+4}\right) \cdot \left( 25z^4+20z^2+4\right) = \\ = 625z^8+500z^6+100z^4+500z^6+400z^4+80z^2+100z^4+80z^2+16 $$ |
| ④ | Combine like terms: $$ 625z^8+ \color{blue}{500z^6} + \color{red}{100z^4} + \color{blue}{500z^6} + \color{green}{400z^4} + \color{orange}{80z^2} + \color{green}{100z^4} + \color{orange}{80z^2} +16 = \\ = 625z^8+ \color{blue}{1000z^6} + \color{green}{600z^4} + \color{orange}{160z^2} +16 $$ |
This page was created using
Simplify polynomials calculator